Inverse Scattering by Perfectly Electric Conducting (PEC) Rough Surfaces: An Equivalent Model With Line Sources

This article presents a new method for the reconstruction of the perfectly electric conducting (PEC) rough surface profiles by utilizing electromagnetic waves. The inaccessible rough surface is illuminated by a tapered plane electromagnetic wave, and the scattered field data are measured on a certain number of points above the surface under test. The method for the inverse electromagnetic imaging problem is based on a special representation of the scattered field in terms of a finite number of fictitious discrete line sources located along a plane below the rough surface. The current densities of these fictitious sources are obtained through the regularized solution of an ill-posed problem. Then, it is shown that the image of the rough surface can be directly retrieved by seeking the points in the space where the tangential component of the total electric field vanishes. Alternatively, a much more rigorous iterative method based on a regularized Newton algorithm is also presented. A comprehensive numerical analysis is provided to demonstrate the feasibility of the presented approach. In this context, the quantitative successes of both approaches are interpreted by considering a very sensitive
$\ell _{2}$
-norm-based error function between the actual and the reconstructed surface profiles. Regarding different scattering scenarios taken into account, the error values obtained for satisfactory reconstructions are generally in the range of 10%–30% for both methods. It is also shown that the presented algorithms are capable of reconstructing the rough surfaces, which oscillate for every
$\lambda $
horizontally and have a peak-to-peak variation of
$0.5\lambda $
at most.